A lock has a 3-number code made up of 15 numbers. If none of the numbers are allowed to repeat, how many different ways can you choose three different numbers in order for a unique code?
Answers
Answer:2730
Step-by-step explanation:
The number of ways we can choose three different numbers in order for a unique code for this case is 2730
How many ways k things out of m different things (m ≥ k) can be chosen if order of the chosen things doesn't matter?We can use combinations for this case,
Total number of distinguishable things is m.
Out of those m things, k things are to be chosen such that their order doesn't matter.
This can be done in total of [tex]^mC_k = \dfrac{m!}{k! \times (m-k)!}[/tex] ways.
If the order matters, then each of those choice of k distinct items would be permuted k! times.
So, total number of choices in that case would be:
[tex]^mP_k = k! \times ^mC_k = k! \times \dfrac{m!}{k! \times (m-k)!} = \dfrac{m!}{ (m-k)!}\\\\^mP_k = \dfrac{m!}{ (m-k)!}[/tex]
This is called permutation of k items chosen out of m items (all distinct).
Given that:
The considered lock as a 3 number codeThere are 15 numbers available.None of the number can repeat.In a lock, the order of the way numbers are arranged matters.
Because of no repetition allowed, we can simulate this situation as:
The number of ways we can choose 3 numbers out of 15 numbers with order = The number of different ways we can choose three different numbers in order for a unique code.
And we have:
The number of ways we can choose 3 numbers out of 15 numbers with order = [tex]^{15}P_3 = \dfrac{15!}{(15-3)!} = \dfrac{15 \times 14 \times 13 \times 12!}{12!} = 2730[/tex]
Thus, the number of ways we can choose three different numbers in order for a unique code for this case is 2730
Learn more about combinations and permutations here:
https://brainly.com/question/16107928
#SPJ2
Related Questions
Which is the graph of f(x) = 3x?
Answers
Step by step:
Rewrite the function as an equation- y=3x
Use slope intercept form to find slope and y-intercept. Slope: 3; Y-Intercept:0,0
susan has a total of 31 books. amy has four less than seven times the number of books compared to susan. write an equation for this situation.
Answers
Answer:
213
Step-by-step explanation:
(31x7)-4
Answer: HURRY I need it quick and will give Brainliest Which value of x satisfies the equation StartFraction 12 over StartRoot x plus 2 EndRoot EndFraction plus 8 equals 10?
Answers
Answer:
D
Step-by-step explanation:
14. The measure of Fis 110. The measure of 2E is 100°
What is the measure of D?
150°
Answers
According to given angles ,
Angle C=180- angle F (Linear pairs or st.line )
=70
Angle B = 180 - angle B (Same as above)
=80
Now
Angle D =Angle C + Angle B (Exterior angle property of a triangle)
=150°
Enjoy
Write an inequality for the graph
Answers
A closed circle means the inequality will be greater than (>) or less than (<)
An arrow pointing right to increasingly positive values means the inequality is getting greater (> or ≥)
A narrowing pointing left to increasingly negative values means the inequality is getting lesser (< or ≤)
So for this graph with an open circle and rightward pointing arrow, “x” will be some number on the number line greater than the first point of -38:
x > -38
2 5/6 times 8 as a mixed number.
Answers
Answer:
lets make it an improper fraction:
17/6 x 8/1(consider 8 over 1) = 22 2/3
Simplify first though
17 x 8 divide by 2 = 4
_____
6 divide by 2 = 3 (8 and 6 are divisible by 2)
Your new simplified multiplication:
17 x 4
_____ then you can do your multiplication across.
3
At the city Museum child admission is $6.40 in adult admission is $9.70 on Sunday 149 tickets were sold for a total sales of $1145 how many adult tickets were sold that day
Answers
Answer:
Adult=58
Step-by-step explanation:
c=child, a=adult
6.4c+9.7a=1145 equation 1
c+a=149 equation 2
a=149-c modified equation 2 to isolate a
6.4c+9.7(149-c)=1145 substitute value of a from equation 1 into equation 2
6.4c+1445.3-9.7c=1145
-3.3c=-300.3
c=91
solve for a
c+a=149
91+a=149
a=58
Check answer:
6.4c+9.7a=1145
6.4(91)+9.7(58)=1145
582.40+562.60=1145
1145=1145
What is the answer to this question
Answers
Solvex2
- 4x=21
using the zero product property.
Answers
Answer:
The answer is (x + 3) (x - 7) = 0
Step-by-step explanation:
x² - 4x = 21
x² - 4x - 21 = 0
x² - 7x + 3x - 21 = 0
x(x - 7) + 3(x - 7) = 0
(x + 3) (x - 7) = 0
Thus, The answer is (x + 3) (x - 7) = 0
-TheUnknownScientist
A community organization wants to determine area support for the construction of a new skate park in the center of town. The organization decides to survey 500 people to see whether they are willing to have their taxes increased for one year to fund the construction of the skate park. What is the best way to randomly choose these 500 people? O Select the first 500 taxpayers listed at the town hall. O Survey the first 500 people who visit the existing skate park. O Assign each taxpayer in town a number and then randomly select 500 of these numbers. O Choose 100 taxpayers from 5 different age groups in town.
PLEASE HELP!!!!
Answers
Answer: I just took the test, and the answer is 'Assign each taxpayer in town a number and then randomly select 500 of these numbers.'
Step-by-step explanation: Happy Pride Month!!
The polynomial f(x) is written in factored form:
f(x) = (x - 6)(x + 5)(x - 9)
What are the zeros of the polynomial function?
O x = 6, x = -5, X = 9
O x = 6, X = 5, X = 9
Ox= -6, X = 5, x = -9
Ox= -6, X = 6, X = -5, x= 5, X = -9, x = 9
15points please help
Answers
Answer:The zeros are 6, -5, 9
Step-by-step explanation:
The zeros of the polynomial function are x = 6, x = -5, and x = 9. The correct option is A.
What are polynomials?In mathematics, a polynomial is an expression that solely uses the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables. It is made up of coefficients and indeterminates.
The zeros of the polynomial function are the values of x that make f(x) equal to zero.
The polynomial f(x) is written in factored form as:
f(x) = (x - 6)(x + 5)(x - 9)
The zeros of the polynomial are the values of x that make any of the factors equal to zero. Therefore, the zeros are:
x - 6 = 0, which gives x = 6
x + 5 = 0, which gives x = -5
x - 9 = 0, which gives x = 9
Thus, the zeros of the polynomial function are x = 6, x = -5, and x = 9.
To know more about polynomials follow
https://brainly.com/question/30385780
#SPJ7
PLEASE HELP!!!!1!1!1! suppose one particular pyramid in egypt has a square base of side length 280 meters and a perpendicular height of 144 meters what is the surgace area of the pyramid?
Answers
Answer:
Pyramid Surface Area = .5 * Perim of Base * Slant Height
Slant Height^2 = 144^2 + 140^2
Slant Height^2 = 20,736 + 19,600
Slant Height^2 = 40,336
Slant Height = 200.8382433701
Surface Area = .5 * perim of base * slant height
Surface Area = .5 * 1,200 * 200.8382433701
Surface Area = 120,503 square meters
Source = www.1728.org/volpyrmd.com
Step-by-step explanation:
Nathan is a recreational cyclist. He can travel 10 miles in one hour on his bicycle. Which graph represents the number of miles Nathan can travel in x hours?
Answers
Answer:
See attachment for graph
Step-by-step explanation:
Given
[tex]1\ hr = 10\ miles[/tex]
Required
The graph that shows the number of miles in x hours
We have:
[tex]1\ hr = 10\ miles[/tex]
Multiply both sides by x
[tex]x * 1hr = 10miles * x[/tex]
[tex]xhr=10x\ miles[/tex]
So, the function is:
[tex]f(x) =10x[/tex]
5x - 2y = 15
2x + 4y = 12
Select the solution to the system from the options below:
Answers
Answer:
7/2, 5/4
Step-by-step explanation:
Answer:
x = 7/2 and y = 5/4
Step-by-step explanation:
2(5x - 2y = 15)
2x + 4y = 12
10x - 4y = 30
2x + 4y = 12 (add)
-----------------
12x = 42
x = [tex]\frac{42}{12}[/tex] = [tex]\frac{7}{2}[/tex]
2x + 4y = 12 (subsitute)
2([tex]\frac{7}{2}[/tex]) + 4y = 12
7 + 4y = 12
4y = 5
y = [tex]\frac{5}{4}[/tex]
What is the measure of arc BC?
Answers
9514 1404 393
Answer:
100°
Step-by-step explanation:
Arc BC is twice the measure of inscribed angle BEC, so is ...
arc BC = 2×50°
arc BC = 100°
Answer:
Step-by-step explanation:
The inscibed angle E is 1/2 the measure of the central angle P so P is 100 degrees, and arc BC is also 100 degrees.
Write at least three expressions that are equivalent to 3(2x - 5)
Answers
Answer:
6x - 15
6x - (5 · 3)
(3 · 2x) - 15
So, for #1, we can just simplify 3(2x - 5) to get another expression:
3(2x - 5),
6x-15
For the next one, we could make a new equation that equals 6x-15:
(3x)+(3x)+(5 *-3)
Then for the last one, how about rewrite it so all of the values are inversely negated?
3(2x - 5),
-3(-2x +5)
I am a line that intersects a circle at 2 points WHAT AM I?
Answers
Some one help will give brain
Answers
Answer:
what the link? didfbdsfaahsdfhsd
Step-by-step explanation:
Anyone can solve this for me thx
Answers
Answer:
16
Step-by-step explanation:
Which expression is equivalent to 128?
Answers
Answer: 2^3 x 2^4
Step-by-step explanation:
The value of the exponential expression is A = 2³.2⁴ = 128
What are the laws of exponents?When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the value of the exponential equation be A
Now , the first expression is p = 2³
The value of p = 8
Now , the second expression is q = 2⁴
The value of q = 16
From the laws of exponents , we get
p.q = 2³.2⁴ = 2³⁺⁴
The value of A = 2⁷ = 128
Hence , the exponential equation is 2⁷ = 128
To learn more about exponents click :
https://brainly.com/question/28966438
#SPJ5
Donnie is packing for a
camping trip. He plans to bring 2 pairs
of shorts and 4 t-shirts. How many
different outfit combinations can he
make?
(No links please :D)
Answers
Answer:
8
Step-by-step explanation:
4x2=8
30)
The variable y is directly proportional to the variable x. If y = 12 when x = 14, what is the value of x when y = 747
Answers
Answer:
871.5
Step-by-step explanation:
directly proportional
y = kx
y = 12 when x = 14
12 = k(14)
k = 12/14
k = 6/7
--------------------------
what is the value of x when y = 747
747 = (6/7) * x
Multiply both sides by 7/6
747 * 7/6 = x
871.5 = x
helppppp! how do I find this?
Answers
Answer:
y=3x-6
Step-by-step explanation:
(2,0). y=mx+b or 0=3 × 2+b, or solving for b: b=0-(3)(2). b=-6.
(3,3). y=mx+b or 3=3 × 3+b, or solving for b: b=3-(3)(3). b=-6.
Plugging in the two points from the graph.
Hence, y=3x-6
len
2. Demetri wakes up at 9:15. It takes him
35 minutes to fold 4 loads of laundry,
35 minutes to bathe the dog, 45 minutes
to bake brownies, and 1 hour to mow the
lawn. After he finishes all of his chores,
he sits down to rest. What time does
Demetri rest?
Answers
Answer:
I think the answer is 11.20 am
ILL GIVE BRAINLIEST PLSSSS HELP BASICALLY EVERYTHING IS IN THE PICTURE IF YOU ANSWER THIS WRONG OR PUT RANDOM WORDS OR A LINK I WILL REPORT YOU FASTER THAN THIS IS DUE
Answers
If you add up all the numbers it equals 50 and then add football and tennis together that equals 13, and then you have to divide 13/50 which equals 0.26 (26%)
Similar Triangles
When are triangles considered similar?
a. corresponding angles are equal AND corresponding sides are proportional
b. corresponding angles are proportional AND corresponding sides are equal
c. corresponding angles are equal OR corresponding sides are proportional
d. corresponding angles are proportional OR corresponding sides are equal
Please select the best answer from the choices provided
Answers
Answer:
A. Corresponding angles are equal AND corresponding sides are proportional
Step-by-step explanation:
I calculated it logically
Answer:
A. Corresponding angles are equal AND corresponding sides are proportional
Enter the values for the highlighted variables to
complete the steps to find the sum:
az
b =
3x 9
+
2x - 6 6 - 2x
CE
d =
3 x
9
+
2x-6 al 2x-6)
3x b.
+
2x-6 2x - 6
3х – с
2x-6
d{x - e)
f(x-3)
= 9
e =
f=
III
g=
DONE
Answers
Answer:
a = - 1
b = - 9
c = 9
d = 3
e = 3
f = 2
g = 3/2
Step-by-step explanation:
For a;
6 - 2x = - (2x - 6)
For b;
-1 * 9 = - 9
For x ;
3x + (-9) = 3x - 9
3x - 9 = d(x - e)
Factorizing :
3(x - 3)
d = 3 ; e = 3
2x - 6 = f(x - 3)
Factorize :
2x - 6 = 2(x - 3)
3(x - 3) / 2(x - 3)
g = 3/2
What is equivalent to 3^-5
Answers
Answer:
The answer is the choose: (D)
[tex] {3}^{ - 5} = \frac{1}{ {3}^{5} } [/tex]
Which figure shows a reflection of pre-image QRS over the line t?
I need help PLSSSSS 50 points!!!
Answers
Fitness can be measured by the rate of oxygen consumption during exercises with more fit people having higher rates. Unfortunately, this measurement is quite costly to obtain, and so an experiment was done to see if this measurement could be predicted from the time it takes (in minutes) to run 1500 m. The following computer output was obtained. Which of the following is NOT CORRECT?
a. For every additional minute it takes to run the 1500 m the estimated oxygen consumption rate decreases by 3.31.
b. The fitted regression line is approximately Y = 82.42(runtime)
c. A person who runs 1500 m in 10 minutes would have an estimated oxygen consumption rate of about 50.
d. There is good evidence that there is a relationship between oxygen consumption and the run time.
e. The slope is 82.42.
Answers
Answer:
b. The fitted regression line is approximately Y = 82.42(runtime)
Step-by-step explanation:
The regression line is Y= aX + b
here b= 82.42 a = -3.31
Hence the regression equation is
Y= 82.42- 3.31 X
where x is the runtime and the slope is given by b.
Option a is correct because from the above equation we see that for every additional minute it takes to run the 1500 m the estimated oxygen consumption rate decreases by 3.31.
Option b is incorrect because the runtime is not given by Y it is given by X.
Option C is correct as
Y= 82.42-3.31*10
Y= 82.42-33.1
Y= 49.32 almost 50
Option d is also correct that the equation line shows a relationship between oxygen consumption and the run time.
Option e is also correct because the slope is given by b and b= 82.42